A 3D visualization system for the distribution of heavy metal pollution in soil based on vertical enhancement interpolation and isosurface rendering

Abstract

This invention discloses a three-dimensional visualization system for soil heavy metal pollution distribution based on vertical enhancement interpolation and isosurface rendering. The spatial interpolation module uses a vertical enhancement factor to scale the vertical coordinates of the original sampling points to obtain transformed three-dimensional coordinates. Based on the transformed three-dimensional coordinates and pollutant concentration data, spatial statistical features are calculated. Based on the stability of these spatial statistical features, either Kriging interpolation or radial basis function interpolation is selected to interpolate the spatial statistical features to obtain a three-dimensional concentration field. The isosurface generation module adaptively determines the density of isosurface levels based on the gradient magnitude of pollutant concentration in the three-dimensional concentration field, and then uses a moving cube algorithm to obtain isosurfaces at different concentration levels. The rendering module assigns transparency values ​​and performs illumination rendering on the isosurfaces at different concentration levels to obtain a three-dimensional image of soil heavy metal pollution distribution. This system provides higher accuracy in three-dimensional characterization of soil heavy metals.

Description

Technical Field

[0001] This invention belongs to the field of soil sampling technology, specifically relating to a three-dimensional visualization system for the distribution of heavy metal pollution in soil based on vertical enhancement interpolation and isosurface rendering. Background Technology

[0002] Heavy metal (HM) pollution in soil has become a major environmental problem, impacting public health and social well-being. Industrial sectors, including chemical manufacturing, oil refining, mining, and tobacco, are major sources of soil pollution. With an estimated five million contaminated sites globally, accurate modeling of the three-dimensional (3D) distribution of soil pollution in industrial areas is crucial.

[0003] Traditional spatial characterization research has evolved from geostatistical interpolation to machine learning prediction, but most methods are still limited to two-dimensional characterization. The literature "Renard P, Courrioux G, 1994. Three-dimensional geometric modeling of a faulted domain: The Soultz Horst example (Alsace, France). Computers & Geosciences 20, 1379-1390" discloses a two-dimensional characterization method, but due to the complex vertical migration and diffusion processes of soil pollutants, two-dimensional characterization is difficult to accurately reflect their distribution patterns in three-dimensional space.

[0004] With the deep integration of computer graphics and spatial analysis technologies, significant progress has been made in 3D visualization techniques based on algorithms such as Kriging interpolation and inverse distance weighting. For example, the paper "Wang M, Zhao W, Wu X, Yang A, Chen Y, Qu Y, Ma J, Wu F, 2025. Advanced three-dimensional prediction model based on stable machine learning for soil pollution: A case study from acontaminated site in Southern China. Journal of Hazardous Materials 494, 138561." discloses an advanced 3D soil pollution prediction model based on stable machine learning, utilizing algorithms such as Kriging interpolation and inverse distance weighting. Notably, the successful application of the moving cube algorithm in contour surface extraction achieves an intuitive reproduction of the spatial distribution pattern of pollutants by constructing a continuous 3D volume model.

[0005] However, the direct application of the aforementioned 3D visualization technologies still faces many serious challenges. Traditional spatial interpolation methods (such as ordinary kriging) are usually based on the isotropic assumption, thus ignoring the geological reality that soil pollution exhibits far greater variability in the vertical direction than in the horizontal direction. When input data becomes sparse due to strict sampling cost constraints, these methods often incorrectly smooth the vertical concentration gradient. This leads to severe morphological distortion and volume deviation in the reconstructed 3D pollution plume along the depth axis, failing to meet the stringent engineering requirements for precise remediation. Therefore, sampling optimization capabilities are crucial. Establishing a collaborative objective function at the 3D scale to simultaneously optimize sampling layout and characterization quality can provide a key solution—effectively reducing economic costs without compromising the accuracy of 3D characterization. Summary of the Invention

[0006] This invention provides a three-dimensional visualization system for the distribution of heavy metal pollution in soil based on vertical enhancement interpolation and isosurface rendering, which provides higher accuracy in the three-dimensional characterization of heavy metals in soil.

[0007] This invention provides a three-dimensional visualization system for the distribution of heavy metal pollution in soil based on vertical enhancement interpolation and isosurface rendering, comprising: The spatial interpolation module is used to scale the vertical coordinates of the original sampling points using a vertical enhancement factor to obtain transformed three-dimensional coordinates. Based on the transformed three-dimensional coordinates and pollutant concentration data, spatial statistical features are calculated. Based on the stability of the spatial statistical features, either Kriging interpolation or radial basis function interpolation is selected to interpolate the spatial statistical features to obtain a three-dimensional concentration field. The isosurface generation module is used to adaptively determine the value density of the isosurface level based on the gradient magnitude of the pollutant concentration in the three-dimensional concentration field, and then use the moving cube algorithm to obtain isosurfaces at different concentration levels. The rendering module is used to assign transparency values ​​and perform lighting rendering on isosurfaces of different concentration levels to obtain a three-dimensional image of the distribution of heavy metal pollution in the soil.

[0008] Preferably, the transformed three-dimensional coordinates are obtained by scaling the vertical coordinates of the original sampling points using a vertical enhancement factor. for: Where λ is the scaling factor. , , These represent the data ranges in the three coordinate directions, respectively. , and These represent the maximum values ​​in the three coordinate directions. , and These are the minimum values ​​in the three coordinate directions, γ represents the vertical coordinate of the original sampling point, and γ is the empirical adjustment coefficient.

[0009] Preferably, spatial statistical characteristics are calculated based on the transformed three-dimensional coordinates and pollutant concentration data, including: First, sampling point pairs are established based on the transformed 3D coordinates and grouped by distance; Secondly, the experimental semivariogram is calculated based on the difference in pollutant concentration data at each sampling point within the group. Then, the nugget value, sill value, and range are obtained by fitting the semivariogram model. At the same time, the mean and variance of the overall and local sub-regions are statistically analyzed. Based on the mean and variance of pollutant concentration, the experimental semivariogram value, and the fitted nugget value, sill value, and range, spatial statistical characteristics are obtained. The spatial statistical characteristics are used to determine whether the sampled data meets the stationarity conditions required for Kriging interpolation, and if not, radial basis function interpolation is switched.

[0010] Preferably, based on the stability of the spatial statistical features, either Kriging interpolation or radial basis function interpolation is selected to interpolate the spatial statistical features to obtain a three-dimensional concentration field, including: The method of combining local statistical consistency test and semivariogram fitting test is used to determine whether the spatial statistical features meet the stationarity condition of Kriging interpolation. If the stationarity condition is met and a stable semivariogram model can be established, the three-dimensional concentration field is generated by Kriging interpolation; otherwise, the three-dimensional concentration field is generated by radial basis function interpolation.

[0011] Preferably, the density of isosurface levels is adaptively determined based on the gradient magnitude of pollutant concentration in the three-dimensional concentration field, including: First, the concentration gradient magnitude of each grid point is calculated based on the three-dimensional concentration field. Then, the concentration range is divided into multiple initial concentration intervals, and the average gradient value of each interval is calculated. Based on the average gradient value, different numbers of isosurface levels are assigned to each interval.

[0012] Preferably, the isosurfaces of different concentration levels are obtained using the moving cube algorithm, including: For each three-dimensional mesh cell, traverse each edge of the three-dimensional mesh cell and calculate the intersection points of the isosurface of the target concentration level with each edge; Then, using the moving cube algorithm, multiple intersection points are organized into triangular patches, and the triangular patches within the three-dimensional mesh unit are spliced ​​together to form an isosurface geometry corresponding to the target concentration level.

[0013] Preferably, the transparency of isosurfaces at different concentration levels is assigned, including: For isosurfaces at different concentration levels, corresponding transparency values ​​are set based on pollutant concentrations, where the first... k Transparency values ​​of isosurfaces for: in, For minimum transparency, For maximum transparency, K is the number of isosurfaces, and β is a nonlinear adjustment parameter.

[0014] Preferably, the isosurfaces at different concentration levels are rendered with illumination, including: First, the Phong lighting model is applied to generate colors with a sense of three-dimensionality and material texture for each triangular facet by comprehensively calculating ambient light, diffuse reflection, and specular highlights. The supersampling anti-aliasing technique is used to render the scene at a higher resolution first, and then the pixel dithering and weighted averaging algorithm is used to downsample to the target resolution, thereby achieving edge smoothing.

[0015] Compared with the prior art, the beneficial effects of the present invention are as follows: By enhancing and scaling the Z-coordinate, this invention amplifies the role of vertical distance in spatial relationship calculations, enabling the interpolation model provided by this invention to more sensitively identify concentration changes between different depth layers, thereby better preserving the vertical heterogeneity and stratified structure of soil pollutants.

[0016] This invention establishes a non-uniform isosurface hierarchy based on the gradient distribution of the pollution concentration field, allowing regions with dramatic gradient changes to correspond to more isosurfaces, thereby enhancing the expressive power of boundaries and internal structures. The so-called "setting denser isosurfaces in regions with significant concentration gradient changes" does not mean temporarily adding patches to a specific local area in space. Instead, it first calculates the concentration gradient distribution based on the interpolated 3D concentration field, then adaptively determines the density of isosurface levels according to the gradient magnitude, and subsequently applies the moving cube algorithm to each of these multiple non-uniformly set isosurface levels, ultimately obtaining a more detailed 3D isosurface representation in key gradient change regions and a simpler representation in gentler regions.

[0017] This application can adaptively allocate isosurface levels based on the intensity of changes in the pollution concentration field, allowing key regions with large concentration gradients to obtain more isosurface levels, thereby improving the accuracy of depicting pollution boundaries, internal layers, and local abrupt structures. Simultaneously, it reduces redundant isosurface levels in gentler regions with smaller concentration gradients, minimizing invalid geometric representations and visual occlusion, and improving the simplicity and readability of the 3D model. Since this process uniformly determines isosurface levels across the entire interpolated 3D concentration field, rather than temporarily supplementing patches for local areas, it also ensures the consistency of the isosurface extraction process and the continuity of the resulting surfaces, thus enhancing the scientific rigor and intuitiveness of subsequent rendering results. Attached Figure Description

[0018] Figure 1 A schematic diagram of the structure of a three-dimensional visualization system for the distribution of heavy metal pollution in soil based on vertical enhancement interpolation and isosurface rendering, provided for a specific embodiment of the present invention; Figure 2 The first set of Cr distribution views provided for a specific embodiment of the present invention; Figure 3 The second set of Cr distribution views provided for a specific embodiment of the present invention; Figure 4 The first set of distribution views of Zn provided in a specific embodiment of the present invention; Figure 5 The second set of distribution views of Zn provided in a specific embodiment of the present invention; Figure 6 The first set of original distribution views of Cr provided for a specific embodiment of the present invention; Figure 7 The second set of original distribution views of Cr provided for a specific embodiment of the present invention; Figure 8 The first set of original distribution views of Zn provided for a specific embodiment of the present invention; Figure 9 The second set of original distribution views of Zn is provided for a specific embodiment of the present invention. Detailed Implementation

[0019] To intuitively present the spatial distribution characteristics of heavy metal pollutants in soil, this invention specifically implements a three-dimensional visualization system for soil heavy metal pollution distribution based on vertical enhancement interpolation and isosurface rendering. This system reconstructs a continuous three-dimensional pollution concentration field from discrete sampling points using a spatial interpolation algorithm, and further utilizes isosurface extraction technology to generate a geometrically explicit volumetric model of the pollutants. Ultimately, it achieves multi-angle and multi-level visualization of the spatial distribution of pollution. The specific structure is as follows: Figure 1 As shown, it includes a spatial interpolation module, an isosurface generation module, and a rendering module.

[0020] The spatial interpolation module provided in this specific embodiment of the invention is used to scale the vertical coordinates of the original sampling points by a vertical enhancement factor to obtain the transformed three-dimensional coordinates. Based on the transformed three-dimensional coordinates and pollutant concentration data, spatial statistical features are calculated. Based on the stability of the spatial statistical features, either Kriging interpolation or radial basis function interpolation is selected to interpolate the spatial statistical features to obtain a three-dimensional concentration field.

[0021] In one specific embodiment, the three-dimensional coordinates provided by the specific embodiment of the present invention for: Where λ is the scaling factor. , , These represent the data ranges in the three coordinate directions, respectively. , and These represent the maximum values ​​in the three coordinate directions. , and These are the minimum values ​​in the three coordinate directions, γ is the vertical coordinate of the original sampling point, and γ is an empirical adjustment coefficient used to balance the weight ratio of the horizontal and vertical directions. In a specific embodiment, γ = 0.5.

[0022] In a specific embodiment of this invention, the vertical coordinates of the original sampling points are recalibrated before interpolation calculation, while the horizontal coordinates remain unchanged. This process improves the insufficient sensitivity of traditional methods in the depth direction because, in most sites, the horizontal scale is usually much larger than the vertical scale. When directly using the original coordinates for interpolation, the contribution of depth differences to spatial distance calculation is too small, which can easily lead to over-smoothing of pollution changes between different soil layers. By enhancing the scaling of the z-coordinate, the role of vertical distance in spatial relationship calculation can be amplified, making the interpolation model more sensitive to identify concentration changes between different depth layers, thereby better preserving the vertical heterogeneity and stratified structure of soil pollution.

[0023] In one specific embodiment, assuming a site has the following parameters: Δx = 200, Δy = 150, Δz = 10, and γ = 0.5, then the vertical enhancement factor is: λ = 200 / 10 × 0.5 = 10. At this point, the original depth z = 3 m will become: z scaled =3×10=30, meaning that within the interpolation model, the depth coordinates of this point are "stretched" by a factor of 10. Thus, two depth points that are only 1 meter apart will appear to differ by 10 units in the model, making it easier to reflect vertical stratification differences.

[0024] Specific embodiments of the present invention calculate spatial statistical features based on transformed three-dimensional coordinates and pollutant concentration data, including: The spatial statistical features provided in this invention mainly refer to statistics used to characterize the spatial correlation and stability of pollutant concentrations. Specifically, these include the mean, variance, experimental semivariogram value, and the fitted nugget value, sill value, and range of the pollutant concentration. The calculation process is as follows: First, sampling point pairs are established based on the transformed three-dimensional coordinates and grouped by distance; second, the experimental semivariogram is calculated based on the difference in pollutant concentration data among the sampling points within each group; then, the semivariogram model is fitted to obtain the nugget value, sill value, and range; simultaneously, the mean and variance of the overall population and local sub-regions are statistically analyzed. Through these spatial statistical features, it can be further determined whether the sampled data meets the stationarity conditions required for Kriging interpolation, and if not, radial basis function interpolation is switched to.

[0025] Based on this, specific embodiments of the present invention automatically select the optimal interpolation algorithm according to data characteristics: Kriging interpolation method considering spatial autocorrelation is preferred, and radial basis function interpolation method is switched when the data does not meet the stationarity assumption, thereby ensuring stable interpolation results under different data conditions.

[0026] Specifically, the spatial statistical features are determined to satisfy the stationarity condition of the Kriging interpolation method by combining the local statistical consistency test and the semivariogram fitting test. When the stationarity condition is satisfied and a stable semivariogram model can be established, the three-dimensional concentration field is generated by the Kriging interpolation method; otherwise, the three-dimensional concentration field is generated by the radial basis function interpolation method.

[0027] The isosurface generation module provided in a specific embodiment of the present invention is used to adaptively determine the value density of the isosurface level based on the gradient magnitude of the pollutant concentration in the three-dimensional concentration field, and then use the moving cube algorithm to obtain isosurfaces at different concentration levels.

[0028] It is understood that, in the specific embodiments of the present invention, "isosurface level" represents the target concentration threshold corresponding to isosurface extraction, which is the input parameter of the moving cube algorithm; "isosurface" is the resulting surface obtained after performing the moving cube algorithm on the corresponding isosurface level. In one specific embodiment, the isosurface generation module provided in this embodiment is used to adaptively determine the value density of the isosurface level based on the gradient magnitude of the pollutant concentration in the three-dimensional concentration field, including: The adaptive determination provided in the specific embodiments of the present invention can be achieved through a non-uniform isosurface level setting method based on gradient weight allocation. Specifically, the gradient distribution of the three-dimensional concentration field is first calculated, then the average gradient value is statistically calculated according to the concentration interval, and the isosurface level interval is negatively correlated with this average gradient value. This results in a smaller isosurface interval being used in concentration intervals with larger gradients, and a larger isosurface interval being used in concentration intervals with smaller gradients, thus forming multiple non-uniformly distributed isosurface levels. The specific process is as follows: First, the concentration gradient magnitude of each grid point is calculated based on the three-dimensional concentration field. Then, the concentration range is divided into multiple initial concentration intervals, and the average gradient value of each interval is calculated. Based on the average gradient value, a different number of isosurface levels are assigned to each interval. The larger the average gradient value, the more isosurface levels are assigned, and the smaller the corresponding isosurface interval, thus generating more isosurfaces in the concentration interval with a larger gradient. Conversely, the smaller the average gradient value, the fewer isosurface levels are assigned, and the larger the corresponding isosurface interval, in order to reduce redundant isosurfaces.

[0029] In one specific embodiment, the moving cube algorithm is used to obtain isosurfaces at different concentration levels, including: For each 3D mesh cell, all edges of the mesh cell are traversed, and the intersections of the isosurface of the target concentration level with each edge are calculated. Then, using the moving cube algorithm, multiple intersections are organized into triangular patches. These triangular patches within the 3D mesh cell are then pieced together to form the isosurface geometry corresponding to the target concentration level. This geometry then enters the transparency assignment and lighting rendering stage to achieve a visual representation of the spatial distribution of pollutants.

[0030] The "multi-level isosurface generation strategy" provided in this invention is not an independent underlying algorithm name detached from the existing technical system; its underlying isosurface extraction still employs the moving cube algorithm. The improvement of this invention lies in the fact that it no longer uses fixed isosurface levels with equal intervals, but rather adaptively sets non-uniform isosurface levels based on the gradient distribution of the pollution concentration field. This allows regions with drastic gradient changes to correspond to more isosurfaces, thereby enhancing the expressive power of boundaries and internal structures. The so-called "setting denser isosurfaces in regions with significant concentration gradient changes" does not mean temporarily adding patches to a specific local area in space. Instead, it involves first calculating the concentration gradient distribution based on the interpolated three-dimensional concentration field, and then adaptively determining the density of isosurface levels based on the gradient magnitude. Specifically, smaller isosurface intervals are used in concentration ranges with larger gradients to generate more isosurfaces; larger isosurface intervals are used in concentration ranges with smaller gradients to reduce redundant isosurfaces. Subsequently, the moving cube algorithm is executed on these multiple non-uniformly set isosurface levels, ultimately obtaining a more detailed three-dimensional isosurface representation in key gradient change regions and a simpler representation in flat regions.

[0031] In a specific embodiment of this invention, the moving cube algorithm is used to extract isosurfaces at different concentration levels based on interpolated 3D mesh data. This algorithm accurately calculates the intersection points of the isosurfaces and the mesh boundaries through linear interpolation. in and These are the coordinates of the two endpoints of the grid boundary. and is the corresponding concentration value, L is the target isosurface level, and P is the calculated intersection coordinates.

[0032] The rendering module provided in the specific embodiment of the present invention is used to assign transparency values ​​and perform lighting rendering on isosurfaces of different concentration levels to obtain a three-dimensional image of the distribution of heavy metal pollution in soil.

[0033] In one specific embodiment, this embodiment assigns transparency values ​​to isosurfaces at different concentration levels, including: For isosurfaces at different concentration levels, corresponding transparency values ​​are set based on pollutant concentrations, where the first... k Transparency values ​​of isosurfaces at each concentration level for: in, For minimum transparency, For maximum transparency, K is the number of isosurfaces, and β is a nonlinear adjustment parameter. In one specific embodiment, Represents minimum transparency. Representing maximum transparency, K = 10 is the total number of isosurfaces, and β = 1.2 is a non-linear adjustment parameter. This parameter design maintains suitable transparency in low-concentration areas while highlighting high-concentration pollution areas, thus effectively revealing the spatial distribution characteristics of pollutants. k represents the isosurface number or index, indicating the transparency value of the k-th isosurface. Assuming a total of K isosurfaces are generated, each isosurface is assigned a number k according to its concentration level or rendering order, and the corresponding transparency is calculated using this number in the formula. As k increases, Gradually from Change to This allows for the rendering of varying transparency across multiple isosurfaces.

[0034] By nonlinearly mapping the isosurface index k to the transparency parameter This enables differentiated visualization of different concentration levels. For low-concentration isosurfaces, their ordinal numbers are smaller, resulting in... Closer Therefore, it exhibits a strong translucent effect, thereby reducing the obstruction of the internal structure; for high-concentration isosurfaces, its serial number is larger. Closer Therefore, it has stronger visibility and more prominent visual performance. At the same time, the nonlinear adjustment parameter β=1.2 makes the transparency change more gradual in low concentration areas, while the transparency of high concentration areas increases more significantly, thus highlighting the core pollution areas while maintaining the overall sense of layering.

[0035] In one specific embodiment, this embodiment performs illumination rendering on isosurfaces with different concentration levels, including: First, the Phong lighting model is applied. This model generates colors with a sense of depth and material texture for each triangular facet by comprehensively calculating ambient light, diffuse reflection (which depends on the angle between the surface normal and the light direction), and specular highlights (simulating surface gloss). Next, to eliminate jagged edges on the isosurface, the system employs supersampling anti-aliasing technology: the scene is first rendered at a higher resolution, and then downsampled to the target resolution using pixel dithering and a weighted averaging algorithm, thus achieving edge smoothing. These post-processing steps transform the original geometric isosurface into a 3D image that combines scientific accuracy with visual expressiveness.

[0036] Traditional interpolation methods often ignore the dramatic vertical changes in soil properties, leading to significant distortion in the depth-axis 3D reconstruction results. This invention, in a specific embodiment, improves the spatial interpolation algorithm by introducing a vertical enhancement factor and combines it with moving cube isosurface extraction technology, successfully reconstructing the fine structure of heavy metal pollution plumes under sparse sampling conditions. Figures 2-9 As shown, the results indicate that for pollutants such as chromium (Cr) and zinc (Zn) with complex spatial heterogeneity, the optimized three-dimensional plume morphology maintains a high degree of consistency with the original distribution and exhibits stable structural characteristics from different perspectives.

[0037] In terms of 3D visualization, specific embodiments of this invention implement several targeted optimizations to the classic moving cubes algorithm. The research utilizes a non-uniform isosurface hierarchy to generate denser isosurfaces in key regions where pollutant concentration gradients change dramatically, thereby accurately depicting the boundaries and internal structure of the pollution plume. In terms of visual presentation, the research breaks away from simple color-filling patterns, introducing a physically based lighting model and transparency gradient technology. The non-linear concentration transparency design allows low-concentration areas to appear semi-transparent without obstructing the view, while high-concentration areas display dense and prominent visual features. The resulting 3D model not only possesses scientific accuracy but also excellent visual intuitiveness and spatial depth, enabling environmental decision-makers to quickly grasp the 3D spatial configuration and migration trends of the pollution plume and accurately locate core problem areas.

Claims

1. A three-dimensional visualization system for the distribution of heavy metal pollution in soil based on vertical enhancement interpolation and isosurface rendering, characterized in that, include: The spatial interpolation module is used to scale the vertical coordinates of the original sampling points using a vertical enhancement factor to obtain transformed three-dimensional coordinates. Based on the transformed three-dimensional coordinates and pollutant concentration data, spatial statistical features are calculated. Based on the stability of the spatial statistical features, either Kriging interpolation or radial basis function interpolation is selected to interpolate the spatial statistical features to obtain a three-dimensional concentration field. The isosurface generation module is used to adaptively determine the value density of the isosurface level based on the gradient magnitude of the pollutant concentration in the three-dimensional concentration field, and then use the moving cube algorithm to obtain isosurfaces at different concentration levels. The rendering module is used to assign transparency values ​​and perform lighting rendering on isosurfaces of different concentration levels to obtain a three-dimensional image of the distribution of heavy metal pollution in the soil.

2. The three-dimensional visualization system for soil heavy metal pollution distribution based on vertical enhancement interpolation and isosurface rendering according to claim 1, characterized in that, The transformed three-dimensional coordinates are obtained by scaling the vertical coordinates of the original sampling points using a vertical enhancement factor. for: Where λ is the scaling factor. , , These represent the data ranges in the three coordinate directions, respectively. , and These represent the maximum values ​​in the three coordinate directions. , and These are the minimum values ​​in the three coordinate directions, γ represents the vertical coordinate of the original sampling point, and γ is the empirical adjustment coefficient.

3. The three-dimensional visualization system for soil heavy metal pollution distribution based on vertical enhancement interpolation and isosurface rendering according to claim 1, characterized in that, Spatial statistical characteristics were calculated based on the transformed three-dimensional coordinates and pollutant concentration data, including: First, sampling point pairs are established based on the transformed 3D coordinates and grouped by distance; Secondly, the experimental semivariogram is calculated based on the difference in pollutant concentration data at each sampling point within the group. Then, the nugget value, sill value, and range are obtained by fitting the semivariogram model. At the same time, the mean and variance of the overall and local sub-regions are statistically analyzed. Based on the mean and variance of pollutant concentration, the experimental semivariogram value, and the fitted nugget value, sill value, and range, spatial statistical characteristics are obtained. The spatial statistical characteristics are used to determine whether the sampled data meets the stationarity conditions required for Kriging interpolation, and if not, radial basis function interpolation is switched.

4. The three-dimensional visualization system for soil heavy metal pollution distribution based on vertical enhancement interpolation and isosurface rendering according to claim 1, characterized in that, Based on the stability of the aforementioned spatial statistical features, either Kriging interpolation or radial basis function interpolation is selected to interpolate the spatial statistical features to obtain a three-dimensional concentration field, including: The method of combining local statistical consistency test and semivariogram fitting test is used to determine whether the spatial statistical features meet the stationarity condition of Kriging interpolation. If the stationarity condition is met and a stable semivariogram model can be established, the three-dimensional concentration field is generated by Kriging interpolation; otherwise, the three-dimensional concentration field is generated by radial basis function interpolation.

5. The three-dimensional visualization system for soil heavy metal pollution distribution based on vertical enhancement interpolation and isosurface rendering according to claim 1, characterized in that, The density of isosurface levels is adaptively determined based on the gradient magnitude of pollutant concentration in a three-dimensional concentration field, including: First, the concentration gradient magnitude of each grid point is calculated based on the three-dimensional concentration field. Then, the concentration range is divided into multiple initial concentration intervals, and the average gradient value of each interval is calculated. Based on the average gradient value, different numbers of isosurface levels are assigned to each interval.

6. The three-dimensional visualization system for soil heavy metal pollution distribution based on vertical enhancement interpolation and isosurface rendering according to claim 1, characterized in that, The moving cube algorithm was used to obtain isosurfaces at different concentration levels, including: For each three-dimensional mesh cell, traverse each edge of the three-dimensional mesh cell and calculate the intersection points of the isosurface of the target concentration level with each edge; Then, using the moving cube algorithm, multiple intersection points are organized into triangular patches, and the triangular patches within the three-dimensional mesh unit are spliced ​​together to form an isosurface geometry corresponding to the target concentration level.

7. The three-dimensional visualization system for soil heavy metal pollution distribution based on vertical enhancement interpolation and isosurface rendering according to claim 1, characterized in that, Assigning transparency values ​​to isosurfaces at different concentration levels, including: For isosurfaces at different concentration levels, corresponding transparency values ​​are set based on pollutant concentrations, where the first... k Transparency values ​​of isosurfaces for: in, For minimum transparency, For maximum transparency, K is the number of isosurfaces, and β is a nonlinear adjustment parameter.

8. The three-dimensional visualization system for soil heavy metal pollution distribution based on vertical enhancement interpolation and isosurface rendering according to claim 1, characterized in that, Illumination rendering of isosurfaces at different concentration levels, including: First, the Phong lighting model is applied to generate colors with a sense of three-dimensionality and material texture for each triangular facet by comprehensively calculating ambient light, diffuse reflection, and specular highlights. The supersampling anti-aliasing technique is used to render the scene at a higher resolution first, and then the pixel dithering and weighted averaging algorithm is used to downsample to the target resolution, thereby achieving edge smoothing.

Images